Finite-dimensional superalgebra realization conjecture for identities with superinvolution

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Let FF be a field of characteristic zero, and let A=A0ˉ⊕A1ˉA=A_{\bar{0}} \oplus A_{\bar{1}} be a finitely generated associative PI-superalgebra over FF with superinvolution.

Finite-dimensional realization conjecture. There exists a finite-dimensional associative superalgebra C=C0ˉ⊕C1ˉC=C_{\bar{0}} \oplus C_{\bar{1}} over FF with superinvolution that satisfies the same identities with superinvolution as AA.

This conjecture proposes a finite-dimensional representative for the identities of every finitely generated associative PI-superalgebra with superinvolution. It is motivated by analogous results for ordinary algebras with involution, but the source gives no resolution of the superinvolution version.

References

Primary source

Irina Sviridova, “Finite basis problem for identities with involution”, arXiv:1410.2233 (2014).

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